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Finite Element
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The Serendipity Family of Finite Elements
The Serendipity Family of Finite Elements,10.1007/s1020801190873,Foundations of Computational Mathematics,Douglas N. Arnold,Gerard Awanou
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The Serendipity Family of Finite Elements
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Douglas N. Arnold
,
Gerard Awanou
We give a new, simple, dimensionindependent definition of the serendipity
finite element
family. The shape functions are the span of all monomials which are linear in at least sr of the variables where s is the degree of the monomial or, equivalently, whose superlinear degree (total degree with respect to variables entering at least quadratically) is at most r. The degrees of freedom are given by moments of degree at most r2d on each face of dimension d. We establish unisolvence and a geometric decomposition of the space.
Journal:
Foundations of Computational Mathematics  FoCM
, vol. 11, no. 3, pp. 337344, 2011
DOI:
10.1007/s1020801190873
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References
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(
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Journal:
Mathematics of Computation  Math. Comput.
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